The numerous benefits offered by diesel engines, compared to gasoline ones, are balanced by a drawback of increasing concern, namely soot emissions. Nowadays, soot emissions can be reduced by physically trapping the particles within on-board diesel particulate filters (DPF). The filter gets progressively loaded by filtering the soot laden flue gases, thus causing an increasing pressure drop, until regeneration takes place. The aim of this work is to develop a fully predictive three-dimensional mathematical model able to accurately describe the soot deposition process into the filter, the consequent gradual modification of the properties of the filter itself (i.e. permeability and porosity), the formation of a soot filtration cake, and the final regeneration step. The commercial computational fluid dynamics (CFD) code Fluent 6.2.16, based on a finite-volume numerical scheme, is used to simulate the gas and particulate flow fields in the DPF, whereas particle filtration sub-models and regeneration kinetics are implemented through user-defined-subroutines (UDS). Model predictions highlight uneven soot deposition profiles in the first steps of the filtration process; however, the very high resistance to the gas flow of the readily formed cake layer determines the evolution into an almost constant layer of soot particles. The ignition of the loaded soot was simulated under different operating conditions, and two regeneration strategies were investigated: a "mild regeneration" at low temperature and oxygen concentration, that operated a spatially homogeneous ignition of the deposited soot, and a "fast regeneration", with an uneven soot combustion along the axial coordinate of the filter, due to strong temperature gradients inside the filter itself. These findings are supported by comparison and validation with experimental data. (C) 2009 Elsevier Ltd. All rights reserved.